The Whale Optimization Algorithm (WOA) is a recently developed meta-heuristic optimization algorithm which is based on the hunting mechanism of humpback whales. Similarly to other meta-heuristic algorithms, the main problem faced by WOA is slow convergence speed. So to enhance the global convergence speed and to get better performance, this paper introduces chaos theory into WOA optimization process. Various chaotic maps are considered in the proposed chaotic WOA (CWOA) methods for tuning the main parameter of WOA which helps in controlling exploration and exploitation. The proposed CWOA methods are benchmarked on twenty well-known test functions. The results prove that the chaotic maps (especially Tent map) are able to improve the performance of WOA.Highlights Chaos has been introduced into WOA to improve its performance. Ten chaotic maps have been investigated to tune the key parameter ‘ p’ of WOA. The proposed CWOA is validated on a set of twenty benchmark functions. The proposed CWOA is validated on a set of twenty benchmark functions. Statistical results suggest that CWOA has better reliability of global optimality.

Grey Wolf Optimizer (GWO) is a very efficient metaheuristic inspired by the hierarchy of the Canis-lupus wolves. It has been extensively employed to a variety of practical applications. Crow Search Algorithm (CSA) is a recently proposed metaheuristic algorithm which mimics the intellectual conduct of crows. In this paper, a hybrid GWO with CSA, namely GWOCSA is proposed which combines the strengths of both the algorithms effectively with the aim to generate promising candidate solutions in order to achieve global optima efficiently. In order to validate the competence of the proposed hybrid GWOCSA, a widely utilized set of 23 benchmark test functions having a wide range of dimensions and varied complexities, is used in this study. The results obtained by the proposed algorithm are compared with ten other algorithms in the literature for verification. The statistical results demonstrate that the GWOCSA outperforms other algorithms including the recent variants of GWO called Enhanced Grey Wolf Optimizer (EGWO) and Augmented Grey Wolf Optimizer (AGWO) in terms of high local optima avoidance ability and fast convergence speed. Furthermore, in order to demonstrate the applicability of the proposed algorithm at solving complex real-world problems, GWOCSA is also employed to solve the feature selection problem as well. The GWOCSA as feature selection approach is tested on 21 widely employed data sets acquired from the University of California at Irvine (UCI) repository. The experimental results are compared to the state-of-the-art feature selection techniques including the native GWO, EGWO and AGWO. The results reveal that the GWOCSA has comprehensive superiority in solving feature selection problem which proves the capability of the proposed algorithm in solving real-world complex problems.

Butterfly Optimization Algorithm (BOA) is a new comer in the category of nature inspired metaheuristic algorithms, inspired from food foraging behavior of the butterflies. Similar to other metaheuristic algorithms, it encounters two probable problems; (1) entrapment in local optima and (2) slow convergence speed. Chaotic maps are one of the best methods to improve the performance of metaheuristic algorithms. In the present study, chaos is introduced into BOA which increases its performance in terms of both local optima avoidance and convergence speed. Ten chaotic maps are employed to enhance the performance of the BOA. The proposed chaotic BOAs are validated on unimodal and multimodal benchmark test functions as well as on engineering design problems. The results indicate that the chaotic maps are able to significantly boost the performance of BOA.